Internal problem ID [932]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime } x^{2} y-\left (-1+y^{2}\right )^{\frac {3}{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(x^2*y(x)*diff(y(x),x)= (y(x)^2-1)^(3/2),y(x), singsol=all)
\[ -\frac {1}{x}+\frac {\left (y \left (x \right )-1\right ) \left (y \left (x \right )+1\right )}{\left (y \left (x \right )^{2}-1\right )^{\frac {3}{2}}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.707 (sec). Leaf size: 111
DSolve[x^2*y[x]*y'[x]== (y[x]^2-1)^(3/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {\left (1+c_1{}^2\right ) x^2-2 c_1 x+1}}{1-c_1 x} y(x)\to \frac {\sqrt {\left (1+c_1{}^2\right ) x^2-2 c_1 x+1}}{-1+c_1 x} y(x)\to -1 y(x)\to 1 y(x)\to -\frac {\sqrt {x^2}}{x} y(x)\to \frac {\sqrt {x^2}}{x} \end{align*}